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Primary LanguageC++MIT LicenseMIT

Physics-based Animation 4860-1081 2023S

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teaser

Lecture at graduate school of information science and technology in the university of Tokyo, spring semester, 2023

ITC-LMS

For Slack and GitHub Classroom invitations

Instructor

Dr. Nobuyuki Umetani

Time

  • Monday 2rd period, 10:25pm - 12:10pm

Course Description

Computer-generated images are everywhere in movies, video games, and VR. This course is an introduction to the techniques to animate objects in computer graphics based on the law of physics. The aim of the course is to get familiar with applied mathematics such as linear algebra, vector analysis, partial differential equations, variational principle, optimization, and numerical analysis through the animation techniques for particle systems, rigid bodies, elastic bodies. There are C++/Python programming assignments to acquire research-oriented graphics programming skills.

Topics:

  • mass-spring simulation
  • rigid body simulation
  • elastic body simulation
  • cloth and hair modeling & simulation
  • collision-detection using spatial hashing
  • finite boundary method

Lecture Schedule

Day Topic Assignment Slide
(1)
Apr. 10		 Introduction
 [1]
(2)
Apr. 17		 Data Structure
data structure for simulation
Implicit surface		 task00 [2]
(3)
Apr. 24		 Time Integration
backward & forward Euler method,
particle system		 task01 [6]
(4)
May 1		 Newtonian Mechanics
 task02 [5]
(5)
May 8		 Collision Detection
principal component analysis
sort & sweep method		 task03 [9]
(6)
May 15		 Optimization
bounding volume hierarchy
Hessian & Jacobian		 task04 [10]
(7)
May 22		 Simple Elastic Energy
Newton-Raphson method
mass-spring system		 task05 [12]
(8)
Jun. 5		 Dynamic Deformation
Variational time integration
 task06 [14]
(9)
Jun. 12		 Linear System Solver
Sparse matrix data structure
Conjugate gradient method		 task07 [17]
(10)
Jun. 19		 Optimization with Constraint
Lagrange multiplier method		 task08 [18]
(11)
Jun. 26		 Rotation
Rotation representation		 task09 [18]
(12)
Jul. 3		 Rigid Body Dynamics
inertia tensor,
angular velocity		 task10 [22]
(13)
Jul. 10		 Continuum Mechanics
tensor,
finite element method		 [24]

Slides

Grading

  • 20% lecture attendance
    • Attendance is counted based on writing a secret keyword on LMS. The keyword is announced for each lecture.
  • 80% small assignments
    • see below

Assignments

There are many small programming assignments. To do the assignments, you need to create your own copy of this repository through GitHub Classroom. These assignements needs to be submitted using pull request functionality of the GitHub. Look at the following document.

How to Submit the Assignments

Task ID Title Thumbnail
task00 Building C++ Program with CMake
task01 Implicit Time Integration
task02 Linear Momentum Conservation
task03 Acceleration of N-body Simulation
task04 Accelerated Nearest Search using Kd-Tree
task05 Gradient Descent for Mass-Spring Simulation
task06 Dynamic Mass-spring System using Variational Euler Time Integration
task07 Solving Laplace Equation with Gauss-Seidel Method
task08 Controlling Volume of a Mesh using Lagrange-Multiplier Method
task09 Rotation and Energy Minimization
task10 Simulation of Rigid Body Precession

Policy

  • Do the assignment by yourself. Don't share the assignments with others.
  • Don't post the answers of the assignment on Slack
  • Late submission of an assignment is subject to grade deduction
  • Score each assignment will not be open soon (instructor needs to adjust weights of the score later)

Reading Material

My Past Lectures